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By Vladimir Mazalov, Dmitry Novikov, Guennady Ougolnitsky, Leon Petrosjan

ISBN-10: 1634834895

ISBN-13: 9781634834896

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Additional resources for Game Theory and Applications: Game-theoretic Models in Mathematical Ecology

Example text

18) The Principle of Coordinated Planning in Control … 35 Remark. By assumption, for each agent Qj(k) ≠  and, moreover, there exist projects with a guaranteed effect to the agent. If not, an agent should design projects with a sufficiently high effect. Example 1. Take 2 subprograms and 2 agents, each having 4 projects. The corresponding parameters are combined in Table 27. Table 27. 8 Suppose that projects 1-4 (projects 5-8) are candidates for inclusion in subprogram 1 (subprogram 2, respectively).

X  X  div(UX )   X X  (v X )   X  S XS t z z   X XZ   X X   X XP; Z  Z  div( UZ )   Z Z  (vZ )   Z  X XZ   Z Z   Z Z ; t z z S  S  div( US )  S S  (vS )   S  D D   S X  B( S p  S )  f ; t z z (5) D  D  div( UD)   D D  (vD )   X X   Z   D D   D DP; t z z P  P  div(U P P)   p P  (vP )   P  D DP   P P t z z   P X XP   P P  uP; u P  u  div(U Pu P )  u u P  (vu P )   u u P t z z  k D gradD  k X gradX.

Obviously, C(v) for sufficiently large  and -core is a subset of the set of preimputations (preimputation is a vector satisfying only the condition of collective rationality). It has the property of stability under the assumption that it is necessary to make the costs equal  for the creation of any coalition. If the original С, but too wide, it can be narrowed by the selection  < 0, which is then interpreted as a reward for the creation of a coalition. The least-core of the game is the intersection of all nonempty -cores.

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Game Theory and Applications: Game-theoretic Models in Mathematical Ecology by Vladimir Mazalov, Dmitry Novikov, Guennady Ougolnitsky, Leon Petrosjan


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